Topics on n-ary algebras

We describe the basic properties of two n-ary algebras, the Generalized Lie Algebras (GLAs) and, particularly, the Filippov (or n-Lie) algebras (FAs), and comment on their n-ary Poisson counterparts, the Generalized Poisson (GP) and Nambu-Poisson (N-P) structures. We describe the Filippov algebra cohomology relevant for the central extensions and infinitesimal deformations of FAs. It is seen that semisimple FAs do not admit central extensions and, moreover, that they are rigid. This extends the familiar Whitehead's lemma to all $n\geq 2$ FAs, n=2 being the standard Lie algebra case. When the n-bracket of the FAs is no longer required to be fully skewsymmetric one is led to the n-Leibniz (or Loday's) algebra structure. Using that FAs are a particular case of n-Leibniz algebras, those with an anticommutative n-bracket, we study the class of n-Leibniz deformations of simple FAs that retain the skewsymmetry for the first n-1 entires of the n-Leibniz bracket.Comment: 11 page

Epigenetic Landscape in Blood Leukocytes Following Ketosis and Weight Loss Induced by a Very Low Calorie Ketogenic Diet (VLCKD) in Patients With Obesity

[Abstract] Background:The molecular mechanisms underlying the potential health benefits of a ketogenic diet areunknown and could be mediated by epigenetic mechanisms.Objective:To identify the changes in the obesity-related methylome that are mediated by the inducedweight loss or are dependent on ketosis in subjects with obesity underwent a very-low calorie ketogenicdiet (VLCKD).Methods:Twenty-one patients with obesity (n¼12 women, 47.9±1.02 yr, 33.0±0.2 kg/m2) after 6months on a VLCKD and 12 normal weight volunteers (n¼6 women, 50.3±6.2 yrs, 22.7±1.5 kg/m2)were studied. Data from the Infinium MethylationEPIC BeadChip methylomes of blood leukocytes wereobtained at time points of ketotic phases (basal, maximum ketosis, and out of ketosis) during VLCKD(n¼10) and at baseline in volunteers (n¼12). Results were further validated by pyrosequencing inrepresentative cohort of patients on a VLCKD (n¼18) and correlated with gene expression.Results:After weight reduction by VLCKD, differences were found at 988 CpG sites (786 unique genes).The VLCKD altered methylation levels in patients with obesity had high resemblance with those fromnormal weight volunteers and was concomitant with a downregulation of DNA methyltransferases(DNMT)1, 3a and 3b. Most of the encoded genes were involved in metabolic processes, protein meta-bolism, and muscle, organ, and skeletal system development. Novel genes representing the top scoringassociated events were identified, includingZNF331,FGFRL1(VLCKD-induced weight loss) andCBFA2T3,C3orf38,JSRP1, andLRFN4(VLCKD-induced ketosis). Interestingly,ZNF331andFGFRL1were validated inan independent cohort and inversely correlated with gene expression.Conclusions:The beneficial effects of VLCKD therapy on obesity involve a methylome more suggestive ofnormal weight that could be mainly mediated by the VLCKD-induced ketosis rather than weight loss.This work was supported by the PronoKal Group® and grants from the Fondo de Investigacion Sanitaria as well as PI17/01287, PI20/00628 and PI20/00650 research projects and CIBERobn from the Instituto de Salud Carlos III (ISCIII)-Subdireccion General de Evaluacion y Fomento de la Investigación; Fondo Europeo de Desarrollo Regional (FEDER) Ana B Crujeiras is funded by a research contract “Miguel Servet” (CP17/00088) from the ISCIII, co-financed by the European Regional Development Fund (FEDER) and Xunta de Galicia-GAIN (IN607B2020)Xunta de Galicia; IN607B202

Development and validation of a population-based prediction scale for osteoporotic fracture in the region of Valencia, Spain: the ESOSVAL-R study

<p>Abstract</p> <p>Background</p> <p>Today, while there are effective drugs that reduce the risk of osteoporotic fracture, yet there are no broadly accepted criteria that can be used to estimate risks and decide who should receive treatment. One of the actual priorities of clinical research is to develop a set of simple and readily-available clinical data that can be used in routine clinical practice to identify patients at high risk of bone fracture, and to establish thresholds for therapeutic interventions. Such a tool would have high impact on healthcare policies. The main objective of the ESOSVAL-R is to develop a risk prediction scale of osteoporotic fracture in adult population using data from the Region of Valencia, Spain.</p> <p>Methods/Design</p> <p><it>Study design</it>: An observational, longitudinal, prospective cohort study, undertaken in the Region of Valencia, with an initial follow-up period of five years; <it>Subjects</it>: 14,500 men and women over the age of 50, residing in the Region and receiving healthcare from centers where the ABUCASIS electronic clinical records system is implanted; <it>Sources of data</it>: The ABUCASIS electronic clinical record system, complemented with hospital morbidity registers, hospital Accidents & Emergency records and the Regional Ministry of Health's mortality register; <it>Measurement of results</it>: Incident osteoporotic fracture (in the hip and/or major osteoporotic fracture) during the study's follow-up period. Independent variables include clinical data and complementary examinations; <it>Analysis</it>: 1) Descriptive analysis of the cohorts' baseline data; 2) Upon completion of the follow-up period, analysis of the strength of association between the risk factors and the incidence of osteoporotic fracture using Cox's proportional hazards model; 3) Development and validation of a model to predict risk of osteoporotic fracture; the validated model will serve to develop a simplified scale that can be used during routine clinical visits.</p> <p>Discussion</p> <p>The ESOSVAL-R study will establish a prediction scale for osteoporotic fracture in Spanish adult population. This scale not only will constitute a useful prognostic tool, but also it will allow identifying intervention thresholds to support treatment decision-making in the Valencia setting, based mainly on the information registered in the electronic clinical records.</p

The Goal Programming as a Tool for Measuring the Sustainability of Agricultural Production Chains of Rice

Agricultural activity is characterized by an intensive use of capital and a considerable dependence on external financing. Access to credit is often limited by the scarcity of resources and lack of guarantees, seriously affecting the productivity and economic performance of agricultural exploitations. The objective of this paper is to assess the sustainability of agricultural production chain of rice in Latin America using multi-criteria analysis tools to facilitate decision-making through a benchmarking process to contribute to their economic sustainability. The implementation of the model in an exploitation typy depending on financing sources (conservative, intermediate, and innovative) has revealed the conflict between the goals, being the intermediate exploitation, which gets the best results. The conclusions show that the flexibilization of financing options positively affects the economic performance

Optimization of flow shop scheduling through a hybrid genetic algorithm for manufacturing companies

A task scheduling problem is a process of assigning tasks to a limited set of resources available in a time interval, where certain criteria are optimized. In this way, the sequencing of tasks is directly associated with the executability and optimality of a preset plan and can be found in a wide range of applications, such as: programming flight dispatch at airports, programming production lines in a factory, programming of surgeries in a hospital, repair of equipment or machinery in a workshop, among others. The objective of this study is to analyze the effect of the inclusion of several restrictions that negatively influence the production programming in a real manufacturing environment. For this purpose, an efficient Genetic Algorithm combined with a Local Search of Variable Neighborhood for problems of n tasks and m machines is introduced, minimizing the time of total completion of the tasks. The computational experiments carried out on a set of problem instances with different sizes of complexity show that the proposed hybrid metaheuristics achieves high quality solutions compared to the reported optimal cases